A Research On The Lattice Boltzmann Method For Its Application In Multi-scale Porous Flows

In recent years,research on flow and heat transfer in porous media is widely used in energy,environmental and chemical engineering etc,such as oil or natural gas mining,hydrogen or carbon dioxide gas storage,combustion and pollution control etc.Numerous studies have shown that the flow inside the porous medium is a multi-scale problem.The research on porous flow can be divided into three parts according to scale: the pore scale,representative elementary volume(REV)scale and macro scale.At the pore scale,the research object is to obtain the detailed flow information in a single or a few pores,and the pore scale approach is usually used to explore the flow and heat transfer mechanism in porous media.The research object of REV scale is a control volume of the porous medium,generally contain more micropores.At the REV scale,the control equations of fluid flow and heat transfer are based on the average physical quantities,such as Darcy's law and the generalized Brinkman-Forchheimer equation.Unlike the pore scale,the REV scale research does not require the detail structure of the medium,but only depends on the statistical parameters of the medium,thus the REV scale approach has high computational efficiency and is suitable for large geometrical scale.Lattice Boltzmann method(LBM)is a numerical method based on mesoscopic scale,which is between macro and micro scale.Compared to the macroscopic method,Lattice Boltzmann method is more convenient for dealing with complex boundary,but also overcomes the size limitation of microscopic calculation method,so that the Lattice Boltzmann method has been widely used in multi-scale flow and heat transfer research in porous media.The main works of this paper are:(1)The basic theory of Lattice Boltzmann method was introduced briefly and detail derivations for recovering Lattice Boltzmann equation to the macroscopic Navier-Stokes(N-S)with the Chapman-Enskog technology were present.Then,the program implementation steps of Lattice Boltzmann method were introduced detailly and the classical square cavity flow was used to verify the accuracy of the basic Lattice Boltzmann model and present procedures.(2)We studied the basic theory of Lattice Boltzmann model for flow in porous media in the REV scale.Firstly,we developed Guo's isothermal incompressible Lattice Boltzmann model for flows in porous media,so that the new model could be restored to the standard compressible generalized Brinkman-Forchheimer equation;secondly,a thermal lattice Boltzmann model,based on the total energy model,was proposed,which can consider the influence of viscous dissipation and compressible work effects,and local thermal non-equilibrium effect in porous media was taken into account in the new model.The two models overcome the limitations of the existing models,and expand the application space of LBM.(3)We studied the basic theory of Lattice Boltzmann method for micro flows.Firstly,a new boundary scheme was put forward to simulate micro flows.The boundary treatment is based on the second-order velocity slip boundary,in which the surface diffusion and slip effects were considered,simultaneously;then,the boundary scheme was used to simulate the methane gas flow in a micro Kerogen channel.(4)The multi-scale adsorption process in porous media was simulated.Firstly,the concentration equation of adsorption gas was derived,and coupling with the Lattice Boltzmann method at the REV scale,the breakthrough curves of adsorption for trace gas were simulated;then,a mathematical model for adsorption in porous medium at the pore scale was established,the diffusion in the solid skeleton was considered in the model;thirdly,based on the D2Q9 speed discrete model,a new boundary scheme for dealing with Robin boundary was proposed and it is suitable for surface adsorption and chemical reaction on the boundary;finally,the new boundary treatment scheme was used to simulate the dynamic adsorption at the pore scale.